ArithMind Mental Arithmetic Lessons
Stage 2 · Phase 1: Foundations beginner children

Single-Digit Mental Subtraction

Master subtracting single-digit numbers mentally using counting back and complement strategies.

Building on Addition

Single-digit mental subtraction means taking away a number from 1 to 9 and finding the difference without written working. The starting number may be larger than one digit: both 9 - 4 and 16 - 7 belong here. This stage follows single-digit addition because subtraction undoes addition. If 8 + 6 = 14, then 14 - 6 = 8 and 14 - 8 = 6. Those connected equations are called a fact family.

Thinking of subtraction as the reverse of addition gives you more than one route to an answer. You can move backward from the starting number, or you can move upward from the number being subtracted. Neither route is automatically best; choose the one that makes the numbers friendly.

A Real Reason to Use It

Imagine you have £14 for a snack and a drink. The snack costs £6. You can work out 14 - 6 mentally and know at once that £8 remains. That helps you decide whether the drink fits your budget before reaching the till. The same skill helps when counting down game points, comparing two scores, or finding how many objects are missing from a set.

Two Useful Mental Routes

The bridge through ten method is helpful when a subtraction crosses 10. For 14 - 6, split 6 into 4 and 2. First do 14 - 4 = 10, then 10 - 2 = 8. The split is not a guess: 4 and 2 still total 6, so the correct amount is removed.

The counting-up complement method uses the previous addition stage directly. For 17 - 9, ask, “What must I add to 9 to reach 17?” Jump 1 to reach 10, then 7 to reach 17. The jumps total 8, so 17 - 9 = 8. Counting up is especially convenient when the numbers are close, as in 12 - 9.

You can also adjust around 10. For 18 - 9, subtract 10 to get 8, then add 1 back because you removed one too many. This is a compact variation of bridging.

Four Examples, Fully Explained

For 13 - 5, bridge through ten: split 5 into 3 + 2, calculate 13 - 3 = 10, and then 10 - 2 = 8.

For 15 - 7, count up from 7: the jump to 10 is 3 and the jump from 10 to 15 is 5. Since 3 + 5 = 8, the difference is 8.

For 12 - 4, ordinary counting back is short enough: 11, 10, 9, 8. Four moves give 8.

For 18 - 9, use the near-ten adjustment: 18 - 10 = 8, then 8 + 1 = 9.

Mistakes to Watch For

A common error is counting the starting number as the first backward move. When subtracting 4 from 12, say 11 on move one, not 12. Another mistake is splitting a number but forgetting the second part; in 13 - 5, stopping at 10 removes only 3. Finally, keep the order clear: 14 - 6 is not the same as 6 - 14.

Check an answer by addition. If you think 16 - 7 = 9, test 9 + 7 = 16. A failed check is useful information, not a reason to feel rushed.

Practice Set

Try these mentally. For four of them, a suggested breakdown is shown.

  1. 9 - 3
  2. 11 - 6 → 11 - 1 - 5
  3. 14 - 8 → 14 - 4 - 4
  4. 17 - 9 → 17 - 10 + 1
  5. 13 - 7
  6. 8 - 5
  7. 16 - 6
  8. 12 - 9 → count up 9 → 10 → 12
  9. 15 - 4
  10. 19 - 7
  11. 10 - 8
  12. 18 - 5
  13. 7 - 2
  14. 16 - 9
  15. 14 - 5
  16. 11 - 3
  17. 20 - 6
  18. 13 - 9

Answer key: 1) 6, 2) 5, 3) 6, 4) 8, 5) 6, 6) 3, 7) 10, 8) 3, 9) 11, 10) 12, 11) 2, 12) 13, 13) 5, 14) 7, 15) 9, 16) 8, 17) 14, 18) 4.

Make Practice Comfortable

Sort practice cards into “known,” “nearly known,” and “needs a method.” Spend most time on the middle group. Say the bridge aloud at first—“four to ten, then two more”—and shorten it only when it feels natural. Mix subtraction with its related addition fact so understanding grows alongside recall.

Quick Questions

Do I always have to cross through 10?

No. Count back for a small subtraction, use a known fact when it comes immediately, or count up when the numbers are close.

What if counting backward makes me lose my place?

Use two larger jumps or hold up one finger for each move. Accuracy matters more than speed.

How do I know I am ready for the next stage?

You are ready when you can solve most differences within 20 and explain or check how you found them. It is fine to keep practising a few stubborn facts.

Practice Examples

Example 1: 13 - 5 = ?

  1. Split 5 into 3 and 2 because 13 - 3 reaches 10
  2. Subtract the first part: 13 - 3 = 10
  3. Subtract the remaining part: 10 - 2 = 8
  4. Check with addition: 8 + 5 = 13

Answer: 8

Example 2: 15 - 7 = ?

  1. Turn the subtraction into the question 7 + ? = 15
  2. Count from 7 to 10, which is 3
  3. Then count from 10 to 15, which is 5
  4. Combine the jumps: 3 + 5 = 8

Answer: 8

Example 3: 12 - 4 = ?

  1. Use counting back because only four steps are needed
  2. Move back one at a time: 12, 11, 10, 9, 8
  3. Four backward moves land on 8
  4. Verify that 8 + 4 returns to 12

Answer: 8

Example 4: 18 - 9 = ?

  1. Notice that subtracting 10 from 18 would give 8
  2. Nine is one less than 10, so add one back
  3. Calculate 8 + 1 = 9
  4. Check the related fact: 9 + 9 = 18

Answer: 9